Um estudo sobre polígonos em Z2

Abstract

The objective of the work is to present a study on the polygons immersed in Z2, since both the polygons and the grid are present in several contexts in Basic Education. The opening chapter provides basic concepts that support the results obtained throughout the work. Then, it is shown that, in addition to the squares, no regular n-agon can be immersed in Z2. We also deal with the area of polygons immersed in Z2, which can be easily calculated when we know the number of points of Z2 located on their sides and inside, through Pick’s Theorem. Finally, we bring the solution to a problem that deals with the immersion of squares in Z2 and some applications of Pick’s Theorem in questions extracted from exams of different academic levels.